Question

The lengths of lumber a machine cuts are normally distributed with a mean of

104

inches and a standard deviation of

0.6

inch.​(a) What is the probability that a randomly selected board cut by the machine has a length greater than

104.14

​inches?​(b) A sample of

42

boards is randomly selected. What is the probability that their mean length is greater than

104.14

​inches?

​(a) The probability is

Answer 1

Solution :

A

Given that,

mean = = 104

standard deviation = = 0.6

P(x > 104.14) = 1 - P(x< 104.14)

= 1 - P[(x -) / < (104.14-104) / 0.6]

= 1 - P(z <0.23 )

Using z table

= 1 -  0.591

probability=0.4090

B.

Given that,

mean = = 104

standard deviation = = 0.6

= =104

= / n = 0.6/ 42 = 0.09

P( >104.14 ) = 1 - P( <104.14 )

= 1 - P[( - ) / < (104.14-104) / 0.09]

= 1 - P(z <1.56 )

Using z table

= 1 - 0.9406

=0.0594